Bohr’s circular orbits

Certain old assumptions die hard, particularly those having to do with circularity of motion. The circle is a sacrosanct figure for many cultures and, though it may be refuted as the actual description of a natural phenomenon, it is never completely abandoned as the ideal for which nature somehow strives. Bohr s circular orbits would give way to other models but the role of the circle itself continued to enlarge. Here we are going to explore, not quantum theory itself but the assumptions on which it is based. These include the circle, or more accurately the sphere, in a prominent role. 

When we apply the de Broglie electron/wave to Bohr s circular orbit (Sec. 1.5), we find some similarities to the particle-in-a-box wavefunction. Those similarities remain, now that we extend the electron s motion to r and 0. For example,... 

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